Fractal species distributions do not produce power-law species-area relationships

We derive the species-area relationship (SAR) expected from an assemblage of fractally distributed species. If species have truly fractal spatial distributions with different fractal dimensions, we show that the expected SAR is not the classical power-law function, as suggested recently in the literature. This analytically derived SAR has a distinctive shape that is not commonly observed in nature: upward-accelerating richness with increasing area (when plotted on log-log axes). This suggests that, in reality, most species depart from true fractal spatial structure. We demonstrate the fitting of a fractal SAR using two plant assemblages (Alaskan trees and British grasses). We show that in both cases, when modelled as fractal patterns, the modelled SAR departs from the observed SAR in the same way, in accord with the theory developed here. The challenge is to identify how species depart from fractality, either individually or within assemblages, and more importantly to suggest reasons why species distributions are not self-similar and what, if anything, this can tell us about the spatial processes involved in their generation.

Implementation of a cogeneration plant for a food processing facility. A case study

The present work presents an investigation regarding the feasibility analysis of a cogeneration plant for a food processing facility with the aim to decrease the cost of energy supply. The monthly electricity and heat consumption profiles are analyzed, in order to understand the consumption profiles, as well as the costs of the current furniture of electricity and gas. Then, a detailed thermodynamic model of the cogeneration cycle is implemented and the investment costs are linked to the thermodynamic variables by means of cost functions. The optimal electricity power of the co-generator is determined with reference to various investment indexes. The analysis highlights that the optimal dimension varies according to the chosen indicator, therefore it is not possible to establish it univocally, but it depends on the financial/economic strategy of the company through the considered investment index.